What is the integral from pi/4 to pi/2 of (sin(x))/x ?

The integral from pi/4 to pi/2 of (sin(x))/x is \Si(pi/2)-\Si(pi/4)

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integral from pi/4 to pi/2 of (sin(x))/x

\int_{\frac{π}{4}}^{\frac{π}{2}} \frac{sin ( x )}{x} d x

Si (\frac{π}{2}) - Si (\frac{π}{4})

Solution steps

\int_{\frac{π}{4}}^{\frac{π}{2}} \frac{sin ( x )}{x} d x

Use the nonelementary integral:

\int \frac{sin ( x )}{x} d x = Si (x)

= [Si (x)]_{\frac{π}{4}}^{\frac{π}{2}}

Compute the boundaries:

Si (\frac{π}{2}) - Si (\frac{π}{4})

= Si (\frac{π}{2}) - Si (\frac{π}{4})

\int_{- 4}^{4} - \frac{1}{5} x^{3} + 5 x d x

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\int_{0}^{2} x^{5} 64 - x^{6} d x

What is the integral from pi/4 to pi/2 of (sin(x))/x ?
The integral from pi/4 to pi/2 of (sin(x))/x is \Si(pi/2)-\Si(pi/4)